Scalable Calibration of Affinity Matrices from Incomplete Observations

Wenye Li
Proceedings of The 12th Asian Conference on Machine Learning, PMLR 129:753-768, 2020.

Abstract

Estimating pairwise affinity matrices for given data samples is a basic problem in data processing applications. Accurately determining the affinity becomes impossible when the samples are not fully observed and approximate estimations have to be sought. In this paper, we investigated calibration approaches to improve the quality of an approximate affinity matrix. By projecting the matrix onto a closed and convex subset of matrices that meets specific constraints, the calibrated result is guaranteed to get nearer to the unknown true affinity matrix than the un-calibrated matrix, except in rare cases they are identical. To realize the calibration, we developed two simple, efficient, and yet effective algorithms that scale well. One algorithm applies cyclic updates and the other algorithm applies parallel updates. In a series of evaluations, the empirical results justified the theoretical benefits of the proposed algorithms, and demonstrated their high potential in practical applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v129-li20b, title = {Scalable Calibration of Affinity Matrices from Incomplete Observations}, author = {Li, Wenye}, booktitle = {Proceedings of The 12th Asian Conference on Machine Learning}, pages = {753--768}, year = {2020}, editor = {Pan, Sinno Jialin and Sugiyama, Masashi}, volume = {129}, series = {Proceedings of Machine Learning Research}, month = {18--20 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v129/li20b/li20b.pdf}, url = {https://proceedings.mlr.press/v129/li20b.html}, abstract = {Estimating pairwise affinity matrices for given data samples is a basic problem in data processing applications. Accurately determining the affinity becomes impossible when the samples are not fully observed and approximate estimations have to be sought. In this paper, we investigated calibration approaches to improve the quality of an approximate affinity matrix. By projecting the matrix onto a closed and convex subset of matrices that meets specific constraints, the calibrated result is guaranteed to get nearer to the unknown true affinity matrix than the un-calibrated matrix, except in rare cases they are identical. To realize the calibration, we developed two simple, efficient, and yet effective algorithms that scale well. One algorithm applies cyclic updates and the other algorithm applies parallel updates. In a series of evaluations, the empirical results justified the theoretical benefits of the proposed algorithms, and demonstrated their high potential in practical applications.} }
Endnote
%0 Conference Paper %T Scalable Calibration of Affinity Matrices from Incomplete Observations %A Wenye Li %B Proceedings of The 12th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Sinno Jialin Pan %E Masashi Sugiyama %F pmlr-v129-li20b %I PMLR %P 753--768 %U https://proceedings.mlr.press/v129/li20b.html %V 129 %X Estimating pairwise affinity matrices for given data samples is a basic problem in data processing applications. Accurately determining the affinity becomes impossible when the samples are not fully observed and approximate estimations have to be sought. In this paper, we investigated calibration approaches to improve the quality of an approximate affinity matrix. By projecting the matrix onto a closed and convex subset of matrices that meets specific constraints, the calibrated result is guaranteed to get nearer to the unknown true affinity matrix than the un-calibrated matrix, except in rare cases they are identical. To realize the calibration, we developed two simple, efficient, and yet effective algorithms that scale well. One algorithm applies cyclic updates and the other algorithm applies parallel updates. In a series of evaluations, the empirical results justified the theoretical benefits of the proposed algorithms, and demonstrated their high potential in practical applications.
APA
Li, W.. (2020). Scalable Calibration of Affinity Matrices from Incomplete Observations. Proceedings of The 12th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 129:753-768 Available from https://proceedings.mlr.press/v129/li20b.html.

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